A collection that contains no duplicate elements. More formally, sets
contain no pair of elements e1 and e2 such that
e1.equals(e2), and at most one null element. As implied by
its name, this interface models the mathematical set abstraction.

The Set interface places additional stipulations, beyond those
inherited from the Collection interface, on the contracts of all
constructors and on the contracts of the add, equals and
hashCode methods. Declarations for other inherited methods are
also included here for convenience. (The specifications accompanying these
declarations have been tailored to the Set interface, but they do
not contain any additional stipulations.)

The additional stipulation on constructors is, not surprisingly,
that all constructors must create a set that contains no duplicate elements
(as defined above).

Note: Great care must be exercised if mutable objects are used as set
elements. The behavior of a set is not specified if the value of an object
is changed in a manner that affects equals comparisons while the object is
an element in the set. A special case of this prohibition is that it is
not permissible for a set to contain itself as an element.

Some set implementations have restrictions on the elements that
they may contain. For example, some implementations prohibit null elements,
and some have restrictions on the types of their elements. Attempting to
add an ineligible element throws an unchecked exception, typically
NullPointerException or ClassCastException. Attempting
to query the presence of an ineligible element may throw an exception,
or it may simply return false; some implementations will exhibit the former
behavior and some will exhibit the latter. More generally, attempting an
operation on an ineligible element whose completion would not result in
the insertion of an ineligible element into the set may throw an
exception or it may succeed, at the option of the implementation.
Such exceptions are marked as "optional" in the specification for this
interface.

toArray

<T> T[] toArray(T[] a)

Returns an array containing all of the elements in this set; the
runtime type of the returned array is that of the specified array.
Obeys the general contract of the
Collection.toArray(Object[]) method.

add

Adds the specified element to this set if it is not already present
(optional operation). More formally, adds the specified element,
o, to this set if this set contains no element
e such that (o==null ? e==null :
o.equals(e)). If this set already contains the specified
element, the call leaves this set unchanged and returns false.
In combination with the restriction on constructors, this ensures that
sets never contain duplicate elements.

The stipulation above does not imply that sets must accept all
elements; sets may refuse to add any particular element, including
null, and throwing an exception, as described in the
specification for Collection.add. Individual set
implementations should clearly document any restrictions on the
elements that they may contain.

remove

Removes the specified element from this set if it is present (optional
operation). More formally, removes an element e such that
(o==null ? e==null : o.equals(e)), if the set contains
such an element. Returns true if the set contained the
specified element (or equivalently, if the set changed as a result of
the call). (The set will not contain the specified element once the
call returns.)

addAll

Adds all of the elements in the specified collection to this set if
they're not already present (optional operation). If the specified
collection is also a set, the addAll operation effectively
modifies this set so that its value is the union of the two
sets. The behavior of this operation is unspecified if the specified
collection is modified while the operation is in progress.

retainAll

Retains only the elements in this set that are contained in the
specified collection (optional operation). In other words, removes
from this set all of its elements that are not contained in the
specified collection. If the specified collection is also a set, this
operation effectively modifies this set so that its value is the
intersection of the two sets.

removeAll

Removes from this set all of its elements that are contained in the
specified collection (optional operation). If the specified
collection is also a set, this operation effectively modifies this
set so that its value is the asymmetric set difference of
the two sets.

equals

Compares the specified object with this set for equality. Returns
true if the specified object is also a set, the two sets
have the same size, and every member of the specified set is
contained in this set (or equivalently, every member of this set is
contained in the specified set). This definition ensures that the
equals method works properly across different implementations of the
set interface.

hashCode

int hashCode()

Returns the hash code value for this set. The hash code of a set is
defined to be the sum of the hash codes of the elements in the set,
where the hashcode of a null element is defined to be zero.
This ensures that s1.equals(s2) implies that
s1.hashCode()==s2.hashCode() for any two sets
s1 and s2, as required by the general
contract of the Object.hashCode method.